For this case we have, by definition, the slope-intercept equation of a line given by:
[tex]y = mx + b[/tex]
Where:
m is the slope
b is the cut point with the y axis
If we are told that the line crosses the axis and in (0,1), we have that[tex]b = 1[/tex]
In addition, they tell us that [tex]m = \frac {4} {5}[/tex]
Substituting in the generic equation we have:
[tex]y = \frac {4} {5} x + 1[/tex]
This is equivalent to:
[tex]y-1 = \frac {4} {5} x[/tex]
[tex]5 (y-1) = 4x\\5y-5 = 4x\\5y-4x = 5[/tex]
Thus, the equation of the line is: [tex]5y-4x = 5[/tex]
ANswer:
Option D
